Rolex stopped working after not wearing it for a few weeks

This watch will keep great time if it has been wound via crown.

Self winding watches need motion ( wrist twist) without they can stop. Sometimes just shake your wrist for a few seconds. I purchased a winder box for times I don't wear. ( Amazon)!
it is belt driven winder, rotates watch 5 minutes every hour.

That's not good, obviously. Who serviced it?
How long ago? Do you have a receipt with warranty of service?
Generally, Rolex's run forever without much service. If an authorized Rolex technician worked on your watch, it would be running like a .... Like a Rolex! Kidding aside, get in touch with the services, nukes you were simply told that by the seller.

Nail on the head. Take it to a good repair/service shop that does Rolex service. Know this, it wont be cheap. But you will get the watch back in great condition and it will run perfect.

This watch is self winding and will stop after 2-3 days if not worn.

To wind it up,shake it from side to side gently for a few minutes (about 100-200 times) and this should wind it up sufficient to make it run for some time.

These watches thrive on being used and if you wish to maintain its operation, wear it at least every other day.

Your Rolex sounds like it has a problem with the automatic winding gear train.A Rolex needs regular servicing when parts can be inspected and replaced.Servicing is about 3-5 year intervals.
You need a specialist Rolex watchmaker as only they can obtain Rolex parts.Try www.rolexrepairs.co.uk a full service will take 2-3 weeks.

Try www.rolexrepairs.co.uk

A Rolex watch is automatic.It needs to be worn 8 hours per day to store enough power to run 36 hours off the wrist.Assuming that you are wearing the watch daily if it still stops there is a problem with the auto winding or mainspring.As a new watch it will be under the Rolex guarantee so return it to the place of purchase.If you dont have a guarantee contact www.rolexrepairs.co.uk for advice or a free estimate.
Regards

this watch will need a service from a rolex trained repairer wich wont be cheap 700 dollars min or 500uk pounds min..you could try tapping watch in palm of hand to see if a batton or luminous paint has come loose,then all it needs is movement taking out and blown clean inside case.any decent repairer can do this.sometimes the teeth on a wheel can wear in one place hence it always stops in same place.recomend service as best action,you never loose on a rolex...